The search for S -matrix axioms

Recent efforts to find a complete set of $S$-matrix axioms are reviewed, emphasis being placed on the impossibility of fitting electromagnetism into the existing framework. It is suggested that a pure $S$-matrix theory may describe an artificial but recognizable world containing all strongly interacting particles but no photons or leptons. The theory would not be self-sufficient because of its failure to provide a mechanism for the measurement of particle momenta (i.e., for experiments that give a meaning to macroscopic space-time), and therein would lie the necessity for electromagnetism. From this viewpoint, the photon mass and the fine structure constant are linked to the theory of measurement and will not emerge from the dynamical bootstrap that determines the strong interaction parameters.